Dribble? Nothing?

[bucky]

Saw this in a pickup game and it started an argument.

A1 leaps into the air and clearly secures a rebound. While descending and still in the air, A1 clearly bats/releases the ball to the floor. After the ball bounces and A1 lands, player A1 clearly secures control of the ball. Player A1 then begins dribbling.

This has been covered but as I type, my brain's memory is frozen. Vaguely recall a case play. Players can't start a dribble without a pivot foot so is there violation here or play on? If play on, what would you call A1's actions...a pass, fumble, dribble, other, or nothing?